Finite Group Databasebeta

← #25080564

Subgroups — #25080564

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D43C211yesmaximal, characteristic, complemented
2#19144077C211yesmaximal, characteristic, complemented
3#19144070C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic, complemented
5#19134042C211yesmaximal, characteristic, complemented
6#19134040C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134036C211yesmaximal, characteristic, complemented
9#19134034C211yesmaximal, characteristic, complemented
10#19134032C211yesmaximal, characteristic, complemented
11#19134030C211yesmaximal, characteristic, complemented
12#19133352C211yesmaximal, characteristic, complemented
13#19133265C211yesmaximal, characteristic, complemented
14#19133261C211yesmaximal, characteristic, complemented
15C43×#1681C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17C2×#13063349—21no—
18C4⋊Q8×D43C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×#10621900C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583244—21no—
25#14583244—21no—
26#14583110C2211yescharacteristic, complemented
27#14583108—21no—
28#14583106C2211yescharacteristic, complemented
29#14583104C2211yescharacteristic, complemented
30#14583102—21no—
31#14583100C2211yescharacteristic
32#14583098—21no—
33#14583096C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583092—21no—
36C8×Dic86C2211yescharacteristic, complemented
37#14583023C2211yescharacteristic, complemented
38D4×C43⋊C8C2211yescharacteristic, complemented
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582951C2211yescharacteristic
42#14582949—21no—
43#14582921C2211yescharacteristic
44#14582921C2211yescharacteristic
45#14582906—21no—
46#14582902—21no—
47#102×D43—21no—
48#102×D43—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#461C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Q8×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72#13063354—44no—
73#13063349—44no—
74C2×Dic172—21no—
75C2×#10621885—21no—
76C2×#10621873—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621882—21no—
80C2×#10621872—21no—
81C2×#10621872—21no—
82C22×C43⋊C8—21no—
83C2×C8×D43D411yescharacteristic
84C2×C8×D43D411yescharacteristic
85#13063325C2311yescharacteristic
86#13063324—21no—
87#13063324—21no—
88#13063323—21no—
89#13063322C2311yescharacteristic
90#13063321—21no—
91#13063321—21no—
92#13063321—21no—
93C4×Dic86C2311yescharacteristic
94#13063290D411yescharacteristic
95D4×Dic43D411yescharacteristic
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—21no—
98#13063283D411yescharacteristic
99#13063281—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43—21no—
102C2×C4×Dic43—21no—
103C42×D43C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063249—21no—
113#13063248—21no—
114#13063247—21no—
115#13063247—21no—
116#13063247—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×SD16×C43—21no—
132C2×D8×C43—21no—
133C22×C8×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159Q8×D43—42no—
160Q8×D43—42no—
161#10621900—22no—
162#10621900D814yes—
163D4×D43—42no—
164D4×D43—42no—
165D4×D43—42no—
166D4×D43—42no—
167D4×D43—82no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×C4×D43—41no—
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43#4111yescharacteristic
175C2×Dic86—21no—
176C2×Dic86—41no—
177C2×Dic86C2×D411yescharacteristic
178SD16×C43—42no—
179D8×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—42no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—21no—
192#10621885—42no—
193#10621883—42no—
194#10621883—42no—
195#10621882—42no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43C2×D411yescharacteristic
209C4×Dic43#4111yescharacteristic
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—42no—
214C2×C43⋊C8C2×D411yescharacteristic
215C2×C43⋊C8C2×D411yescharacteristic
216Dic172—42no—
217#10621873—42no—
218#10621872—42no—
219#10621872—42no—
220C8×D43—41no—
221C8×D43—41no—
222C23×C43—21no—
223C23×C43—41no—
224C22×D43—41no—
225C22×D43—82no—
226C22×D43—82no—
227C22×D43—82no—
228C22×D43#12111yescharacteristic
229Q8×C43—41no—
230Q8×C43—41no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—81no—
237D4×C43C2×D812yes—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C22⋊D43—24no—
246C22⋊D43—82no—
247C22⋊D43—82no—
248C22⋊D43—82no—
249C2×Dic43—21no—
250C2×Dic43—24no—
251C2×Dic43—21no—
252C2×Dic43—42no—
253C2×Dic43—41no—
254C2×Dic43#12111yescharacteristic
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262C4×D43—21no—
263C4×D43—21no—
264C4×D43—22no—
265C4×D43—82no—
266C4×D43C2×D812yes—
267C4×D43#13512yes—
268Dic86—21no—
269Dic86—41no—
270Dic86—41no—
271Dic86—82no—
272Dic86C2×D812yes—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283#19276—431nomaximal, Sylow
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×#12111yescharacteristic
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—164no—
297C2×D43#46612yes—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43C22×D811yescharacteristic
302C4×C43C2×#13511yescharacteristic
303C4×C43#57511yescharacteristic
304C4×C43#57511yescharacteristic
305Dic43—21no—
306Dic43—22no—
307Dic43—41no—
308Dic43—81no—
309Dic43#46612yes—
310Dic43#47112yes—
311C2×#486—431no—
312#3039—431no—
313#3038—431no—
314C8×#41—431no—
315#1682—431no—
316#1682—431no—
317#1682—431no—
318#1682—431no—
319#1681—431no—
320#1681—431no—
321#1681—431no—
322#1681D4311yescharacteristic, complemented
323#1567—431no—
324#1546—431no—
325#1545—431no—
326C2×C43—42no—
327C2×C43—161no—
328C2×C43#304011yescharacteristic
329C2×C43C2×#46611yescharacteristic
330C2×C43C2×#47111yescharacteristic
331D43—22no—
332D43—161no—
333C2×#137—861no—
334C2×AGL(1,ℤ/8)—861no—
335C2×C4⋊Q8—431no—
336C2×#127—431no—
337C4×#41—431no—
338#486—431no—
339#486—431no—
340#486—431no—
341#486—861no—
342#486—861no—
343#486C2×D4311yescharacteristic
344#462—431no—
345#462—431no—
346#462—861no—
347#461—431no—
348#461—861no—
349#461C2×D4311yescharacteristic, complemented
350#460—431no—
351#460—431no—
352#460—861no—
353#459—431no—
354#459—861no—
355#459C2×D4311yescharacteristic
356C8×Q8—431no—
357C8×Q8—431no—
358C8×D4—431no—
359C8×D4—861no—
360C8×D4—861no—
361C8×D4C2×D4311yescharacteristic, complemented
362#431—431no—
363#431—861no—
364#423—431no—
365#423—431no—
366#419—861no—
367#418—861no—
368C2×#102—861no—
369C2×#102—861no—
370C2×C4×C8—431no—
371C2×C4×C8—861no—
372#335—431no—
373#335—431no—
374#335—431no—
375#335C2×D4311yescharacteristic, complemented
376#332—431no—
377#332—431no—
378#332—431no—
379#332C2×D4311yescharacteristic, complemented
380#331—431no—
381#331—431no—
382#331—431no—
383#331C2×D4311yescharacteristic
384C43#1927611yescharacteristic, complemented, Sylow
385C2×#41—431no—
386C22×Q8—861no—
387C22×D4—861no—
388C22×D4—861no—
389C22×D4—861no—
390#137—1724no—
391AGL(1,ℤ/8)—1724no—
392C2×Q16—861no—
393C2×Q16—861no—
394C2×SD16—21no—
395C2×SD16—861no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×D8—21no—
399C2×D8—861no—
400C2×M16—861no—
401C2×M16—861no—
402C22×C8—21no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—861no—
406C4⋊Q8—431no—
407C4⋊Q8—861no—
408C4⋊Q8—861no—
409C4⋊Q8—861no—
410C4⋊Q8C22×D4311yescharacteristic
411#127—431no—
412#127—861no—
413#127—861no—
414#127—861no—
415#127C22×D4311yescharacteristic
416C4×Q8—431no—
417C4×Q8—431no—
418C4×D4—431no—
419C4×D4—861no—
420C4×D4—861no—
421C4×D4C22×D4311yescharacteristic
422#117—431no—
423#117—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C42—431no—
427C2×C42—861no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437C4⋊C8C22×D4311yescharacteristic
438#103—21no—
439#103—861no—
440#103—861no—
441#103—861no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454C22⋊C8—21no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—861no—
461C4×C8—861no—
462C4×C8—861no—
463C4×C8C22×D4311yescharacteristic
464C24—1721no—
465#41—434no—
466#41—862no—
467C2×Q8—21no—
468C2×Q8—431no—
469C2×Q8—861no—
470C2×Q8—1721no—
471C2×Q8—1722no—
472C2×Q8—1722no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—3442no—
481C2×D4—1722no—
482C2×D4—1722no—
483C2×D4—1721no—
484C2×D4—1721no—
485C2×D4—1721no—
486C2×D4—1722no—
487C2×D4—1722no—
488C2×D4D4×D4311yescharacteristic
489C22×C4—21no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—1721no—
496Q16—1722no—
497Q16—1722no—
498SD16—42no—
499SD16—1722no—
500SD16—1722no—
501SD16—1722no—
502D8—42no—
503D8—1722no—
504M16—1722no—
505M16—1722no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—42no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—1721no—
516C2×C8—1721no—
517C2×C8—1722no—
518C2×C8D4×D4311yescharacteristic
519C2×C8D4×D4311yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—431no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—1721no—
528C4⋊C4—1721no—
529C4⋊C4D4×D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—861no—
537C42—861no—
538C42—861no—
539C42C23×D4311yescharacteristic
540C23—21no—
541C23—41no—
542C23—431no—
543C23—3442no—
544C23—3442no—
545C23—3442no—
546C23—1721no—
547Q8—41no—
548Q8—41no—
549Q8—432no—
550Q8—861no—
551Q8—3442no—
552Q8—1721no—
553Q8—1721no—
554D4—21no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—864no—
561D4—3441no—
562D4—3442no—
563D4—3442no—
564D4—3442no—
565D4—1721no—
566D4—1721no—
567D4—1721no—
568D4—1721no—
569D4D8×D4312yes—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—431no—
579C2×C4—862no—
580C2×C4—864no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—3442no—
586C2×C4—1722no—
587C2×C4—1721no—
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C8—21no—
592C8—21no—
593C8—41no—
594C8—41no—
595C8—41no—
596C8—861no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—432no—
608C22—861no—
609C22—861no—
610C22—3441no—
611C22—3441no—
612C22—3441no—
613C22—6884no—
614C22#121×D4311yescharacteristic
615C4—21no—
616C4—41no—
617C4—81no—
618C4—432no—
619C4—432no—
620C4—861no—
621C4—862no—
622C4—3441no—
623C4—1721no—
624C4C2×D8×D4311yescharacteristic
625C4#135×D4311yescharacteristic
626C4#1458369511yescharacteristic
627C4#1458369611yescharacteristic
628C2—42no—
629C2—161no—
630C2—862no—
631C2—6881no—
632C2#1914408411yescharacteristic
633C2#466×D4311yescharacteristic
634C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1681C2
socleC22×C43C2×#121
prime radical#19144070C2
hypercenter#1681D43
hypocenterC43#19276
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1681

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #486×D43C2semidirect
2. #19144077C2semidirect
4. C8×#10621900C2semidirect
5. #19134042C2semidirect
6. #19134040C2semidirect
7. #19134038C2semidirect
8. #19134036C2semidirect
9. #19134034C2semidirect
10. #19134032C2semidirect
11. #19134030C2semidirect
12. #19133352C2semidirect
13. #19133265C2semidirect
14. #19133261C2semidirect
15. C43×#1681C2semidirect
26. #14583110C22semidirect
28. #14583106C22semidirect
29. #14583104C22semidirect
36. C8×Dic86C22semidirect
37. #14583023C22semidirect
38. D4×C43⋊C8C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#461C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
322. #1681D43semidirect
349. #461C2×D43semidirect
361. C8×D4C2×D43semidirect
375. #335C2×D43semidirect
379. #332C2×D43semidirect
384. C43#19276semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#486×D432
#191440772
#191440702
C8×#106219002
#191340422
#191340402
#191340382
#191340362
#191340342
#191340322
#191340302
#191333522
#191332652
#191332612
C43×#16812
#1927643